No they should not sue.

Since it was not the only air station to air those "inaccurate and offensive names" they do not have the right just to sue that one company. Also the constitutional allows freedom of the press therefore even if they did mean to air those names, they have the right to do so if they see fit.

They retracted the names, it's over with

The station has already felt enough of a loss for reporting the names without a lawsuit coming in their direction. Their credibility took a major hit when they were careless enough to report such an obviously fabricated list of pilot names, they're going to have to carry that black eye for a long time and while there is a case for negligence it's kind of past the window that it would be appropriate now.